Combining Texts

All the ideas for 'Frege's Theory of Numbers', 'Varieties of Causation' and 'Ordinatio'

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7 ideas

6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
Parsons says counting is tagging as first, second, third..., and converting the last to a cardinal [Parsons,C, by Heck]
     Full Idea: In Parsons's demonstrative model of counting, '1' means the first, and counting says 'the first, the second, the third', where one is supposed to 'tag' each object exactly once, and report how many by converting the last ordinal into a cardinal.
     From: report of Charles Parsons (Frege's Theory of Numbers [1965]) by Richard G. Heck - Cardinality, Counting and Equinumerosity 3
     A reaction: This sounds good. Counting seems to rely on that fact that numbers can be both ordinals and cardinals. You don't 'convert' at the end, though, because all the way you mean 'this cardinality in this order'.
8. Modes of Existence / E. Nominalism / 1. Nominalism / b. Nominalism about universals
A universal is not a real feature of objects, but only a thought-object in the mind [William of Ockham]
     Full Idea: I maintain that a universal is not something real that exists in a subject [of inherence], either inside or outside the mind, but that it has being only as a thought-object in the mind.
     From: William of Ockham (Ordinatio [1320], DII Qviii prima redactio)
     A reaction: [A footnote says that William later abandoned this view] I don't see a clear distinction here between having real existence in the mind, and being a thought-object in the mind. Maybe we should say 'merely' a thought-object?
9. Objects / D. Essence of Objects / 12. Essential Parts
Mereological essentialism says an entity must have exactly those parts [Sosa]
     Full Idea: Mereological essentialism says that nothing else could have been the unique entity composed of certain parts except the very thing that is composed of those parts.
     From: Ernest Sosa (Varieties of Causation [1980], 2)
     A reaction: This sounds initially implausible. It means the ship of Theseus ceases to be that ship if you change a single nail of it. Whether we say that seems optional, but if we do, it leads to the collaps of all our normal understanding of identity.
18. Thought / E. Abstraction / 2. Abstracta by Selection
A universal is the result of abstraction, which is only a kind of mental picturing [William of Ockham]
     Full Idea: A universal is not the result of generation, but of abstraction, which is only a kind of mental picturing.
     From: William of Ockham (Ordinatio [1320], DII Qviii prima redactio)
     A reaction: The phrase 'mental picturing' works very plausibly for the universal 'giraffe', but not so well for 'multiplication' or 'contradiction'. Though we might broaden 'picturing' to being a much less visual concept. Mapping seems basic.
26. Natural Theory / C. Causation / 9. General Causation / b. Nomological causation
What law would explain causation in the case of causing a table to come into existence? [Sosa]
     Full Idea: If I fasten a board onto a tree stump, causing a table to come into existence, ...what law of nature or, even, what quasi-law or law-like principle could possibly play in such a case of generation the role required by nomological accounts?
     From: Ernest Sosa (Varieties of Causation [1980], 1)
     A reaction: A very nice question. The nomological account is at its strongest when rocks fall off walls or magnets attract, but all sorts of other caused events seem too messy or complex or original to fit the story.
26. Natural Theory / C. Causation / 9. General Causation / d. Causal necessity
Where is the necessary causation in the three people being tall making everybody tall? [Sosa]
     Full Idea: It is not clear how to analyse the form of necessary causation found in the only three people in the room being tall causing everybody in the room to be tall.
     From: Ernest Sosa (Varieties of Causation [1980], 5)
     A reaction: I would want to challenge this as a case of causation. There are no events or processes involved. It seems that a situation described in one way can also be described in another.
The necessitated is not always a result or consequence of the necessitator [Sosa]
     Full Idea: The necessitated is not always a result or consequence of the necessitator. If p-and-q is a fact, then this necessitates that p, but the fact that p need not be a result or consequence of the fact that p-and-q.
     From: Ernest Sosa (Varieties of Causation [1980], p.242)
     A reaction: This is obviously correct, and needs to be borne in mind when considering necessary causation. It is not enough to produce a piece of logic; something in the link from cause to effect must be demonstrated to be necessary.